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zepelin [54]
3 years ago
8

Simplify to create an equivalent expression. 2(3r+7)−(2+r)

Mathematics
1 answer:
tamaranim1 [39]3 years ago
7 0

2(3r+7)−(2+r)

Use distributive property:

6r + 14 - 2 - r

Simplify by combining like terms:

5r +12

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0.87$ per unit ........

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4. Calculate using the order of operations.<br>a) (+30) / (-10) + (-20) / (-1)​
umka2103 [35]

Answer:

17

Step-by-step explanation:

30/-10 + -20/-1

= -3+20

= 17

6 0
3 years ago
2ᵃ = 5ᵇ = 10ⁿ.<br> Show that n = <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bab%7D%7Ba%20%2B%20b%7D%20" id="TexFormula1" titl
11Alexandr11 [23.1K]
There are two ways you can go about this: I'll explain both ways.
<span>
</span><span>Solution 1: Using logarithmic properties
</span>The first way is to use logarithmic properties.

We can take the natural logarithm to all three terms to utilise our exponents.

Hence, ln2ᵃ = ln5ᵇ = ln10ⁿ becomes:
aln2 = bln5 = nln10.

What's so neat about ln10 is that it's ln(5·2).
Using our logarithmic rule (log(ab) = log(a) + log(b),
we can rewrite it as aln2 = bln5 = n(ln2 + ln5)

Since it's equal (given to us), we can let it all equal to another variable "c".

So, c = aln2 = bln5 = n(ln2 + ln5) and the reason why we do this, is so that we may find ln2 and ln5 respectively.

c = aln2; ln2 = \frac{c}{a}
c = bln5; ln5 = \frac{c}{b}

Hence, c = n(ln2 + ln5) = n(\frac{c}{a} + \frac{c}{b})
Factorise c outside on the right hand side.

c = cn(\frac{1}{a} + \frac{1}{b})
1 = n(\frac{1}{a} + \frac{1}{b})
\frac{1}{n} = \frac{1}{a} + \frac{1}{b}

\frac{1}{n} = \frac{a + b}{ab}
and thus, n = \frac{ab}{a + b}

<span>Solution 2: Using exponent rules
</span>In this solution, we'll be taking advantage of exponents.

So, let c = 2ᵃ = 5ᵇ = 10ⁿ
Since c = 2ᵃ, 2 = \sqrt[a]{c} = c^{\frac{1}{a}}

Then, 5 = c^{\frac{1}{b}}
and 10 = c^{\frac{1}{n}}

But, 10 = 5·2, so 10 = c^{\frac{1}{b}}·c^{\frac{1}{a}}
∴ c^{\frac{1}{n}} = c^{\frac{1}{b}}·c^{\frac{1}{a}}

\frac{1}{n} = \frac{1}{a} + \frac{1}{b}
and n = \frac{ab}{a + b}
4 0
3 years ago
Conversion problem for pharmacy
Kipish [7]
Use Google or Wolfram Alpha
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3 years ago
What is the largest integer value of x such that the value of f(x) = x ^ 2 - 6x + 40 exceeds the value of g(x) =; 2 * (1.5) ^ x
baherus [9]

Answer:

1

Step-by-step explanation:

2#&&#&÷&7*÷**#*×*×*÷(×(×¥=111

7 0
2 years ago
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